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A229441
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Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
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1
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6, 14, 37, 109, 324, 915, 2402, 5843, 13229, 28071, 56234, 107080, 194989, 341334, 576993, 945488, 1506848, 2342300, 3559899, 5301215, 7749202, 11137381, 15760476, 21986649, 30271487, 41173901, 55374104, 73693842, 97119059, 126825184
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OFFSET
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1,1
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = (1/5760)*n^8 + (1/2016)*n^7 + (1/576)*n^6 + (11/360)*n^5 + (409/5760)*n^4 + (49/288)*n^3 + (41/96)*n^2 + (2771/840)*n + 2.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(6 - 40*x + 127*x^2 - 224*x^3 + 255*x^4 - 177*x^5 + 77*x^6 - 19*x^7 + 2*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
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EXAMPLE
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Some solutions for n=4:
..0..2..2..2....0..0..0..0....0..2..2..2....0..0..2..2....0..0..0..0
..1..0..0..0....1..1..1..1....1..0..2..2....0..0..2..2....1..1..1..1
..1..0..0..0....1..1..1..1....2..1..0..2....1..1..0..0....2..2..2..2
..1..1..1..1....2..2..2..2....2..2..1..0....2..2..1..1....2..2..2..2
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CROSSREFS
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Column 4 of A229445.
Sequence in context: A272548 A036387 A053560 * A119874 A344380 A270127
Adjacent sequences: A229438 A229439 A229440 * A229442 A229443 A229444
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Sep 23 2013
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STATUS
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approved
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